Chapter 2.2, Problem 25PSC

To determine

To calculate: measure of complement of the angle.

Answer to Problem 25PSC

  ${70}^{\circ }$

Explanation of Solution

Given information: supplement of an angle is ${60}^{\circ }$ less twice the supplement of the complement of the angle.

Formula Used: supplement of an angle $x^{\circ }$ is ${(180-x)}^{\circ }$ and complement is ${(90-x)}^{\circ }$ .

Calculation: let measure of the angle be $x^{\circ }$ then its supplement is ${(180-x)}^{\circ }$ supplement of complement is ${\{180-(90-x)\}}^{\circ }={(90+x)}^{\circ }$ . Now according to given conditions.

  $\begin{array}{l}$ {({180}^{\circ }-x)}^{\circ }+{60}^{\circ }=2{(90+x)}^{\circ }$180-x+{60}^{\circ }={180}^{\circ }+2x^{\circ }\\ 3x^{\circ }={60}^{\circ }\\ \therefore x={20}^{\circ }\end{array}$

  $\therefore$ Its complement is ${90}^{\circ }-{20}^{\circ }={70}^{\circ }$